So much Numbers

1st Solution $$ Suppose $$ $A = 1 + 2 + 3 + ... + 10000$ , then $$ $A = 10000 + 9999 + 9998 + ... + 1$ $$ -------------------------------------------------- + $$ $2A = 10001 \times 10000$ $$ $A = 10001 \times 5000 = 50005000$ $$ $$ 2nd Solution $$ ${ S }_{ n }\quad =\quad \frac { n }{ 2 } \quad (a\quad +\quad { U }_{ n })$ ${ S }_{ 10000 }\quad =\quad 5000\quad (1\quad +\quad 10000)\quad =\quad 5000\quad \times \quad 10001\quad =\quad 50005000$ 3rd Solution $$ ${ S }_{ n }\quad =\quad \frac { n }{ 2 } \quad (2a\quad +\quad (n\quad -\quad 1)b)$ ${ S }_{ 10000 }\quad =\quad 5000\quad (2\quad +\quad 9999)\quad =\quad 5000\quad \times \quad 10001\quad =\quad 50005000$